Related papers: Discrete series multiplicities for classical group…

We consider the problem of explicitly computing dimensions of spaces of automorphic or modular forms in level one, for a split classical group $\mathbf{G}$ over $\mathbb{Q}$ such that $\mathbf{G}(\R)$ has discrete series. Our main…

We determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GL_n over Q of any given infinitesimal character, for essentially all n <= 8. For this, we compute the dimensions of spaces of level 1…

Let $G$ be a connected semisimple simply connected Lie group with a compact Cartan subgroup and let $\Gamma$ be a uniform lattice in $G$. Let $\widehat{G}_d$ denote the set of equivalence classes of unitary discrete series representations…

Quaternionic automorphic representations are one attempt to generalize to other groups the special place holomorphic modular forms have among automorphic representations of $\mathrm{GL}_2$. Here, we use "hyperendoscopy" techniques to…

Assume $G$ is a connected reductive algebraic group defined over $\bar{\mathbb{F}_p}$ such that $p$ is good prime for $G$. Furthermore we assume that $Z(G)$ is connected and $G/Z(G)$ is simple of classical type. Let $F$ be a Frobenius…

We prove several dimension formulas for spaces of scalar-valued Siegel modular forms of degree $2$ with respect to certain congruence subgroups of level $4$. In case of cusp forms, all modular forms considered originate from cuspidal…

We prove classification results for the cuspidal automorphic algebraic representations of ${\rm GL}_n$ over $\mathbb{Q}$ ($n$ arbitrary) of small prime conductor and small motivic weight, in the spirit of the works of Chenevier, Lannes and…

We carry out some computations of vector valued Siegel modular forms of degree two, weight (k,2) and level one. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an…

We prove an explicit integral representation -- involving the pullback of a suitable Siegel Eisenstein series -- for the twisted standard $L$-function associated to a holomorphic vector-valued Siegel cusp form of degree $n$ and arbitrary…

In this paper, we consider automorphic forms on $\mathrm{Sp}_4(\mathbb{A}_\mathbb{Q})$ which generate large discrete series representations of $\mathrm{Sp}_4(\mathbb{R})$ as $(\mathfrak{sp}_4(\mathbb{R}),K_\infty)$-modules. We determine the…

We obtain an asymptotic formula for a weighted sum over cuspidal eigenvalues in a specific region, for $\SL_2$ over a totally real number field $F$, with discrete subgroup of Hecke type $\Gamma_0(I)$ for a non-zero ideal $I$ in the ring of…

In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for general semisimple algebraic group $G$ defined over a number field $k$ such that its Archimedean…

The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this…

Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of arbitrary automorphic forms on $G(\mathbb…

In this paper, we prove the existence of an efficient algorithm for the computation of $q$-expansions of modular forms of weight $k$ and level $\Gamma$, where $\Gamma \subseteq SL_{2}({\mathbb{Z}})$ is an arbitrary congruence subgroup. We…

Let $q$ be an odd power of a prime $p\in \mathbb{N}$, and $\mathrm{PPSP}(\sqrt{q})$ be the finite set of isomorphism classes of principally polarized superspecial abelian surfaces in the simple isogeny class over $\mathbb{F}_q$…

This paper deals with a new analytic type of vector- and Clifford algebra valued automorphic forms in one and two vector variables. For hypercomplex generalizations of the classical modular group and their arithmetic congruence subgroups…

This thesis provides an explicit, general trace formula for the Hecke and Casimir eigenvalues of GL(2)-automorphic representations over a global field. In special cases, we obtain Selberg's original trace formula. Computations for the…

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

This paper contains two parts toward studying abelian varieties from the classification point of view. In a series of papers, the current authors and T.-C. Yang obtain explicit formulas for the numbers of superspecial abelian surfaces over…